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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 123–140 (Mi timm814)  

Analysis of the Bloch equations for the nuclear magnetization model

L. A. Kalyakin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We consider a system of three ordinary first-order differential equations known in the theory of nuclear magnetism as the Bloch equations. The system contains four dimensionless parameters as coefficients. Equilibrium states and the dependence of their stability on these parameters is investigated. The possibility of the appearance of two stable equilibrium states is discovered. The equations are integrable in the absence of dissipation. For the problem with small dissipation far from equilibrium, approximate solutions are constructed by the method of averaging.

Keywords: nonlinear equations, equilibrium, dissipation, stability, asymptotics, averaging.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 281, suppl. 1, 64–81

Bibliographic databases:

Document Type: Article
UDC: 517.928
Received: 10.10.2011

Citation: L. A. Kalyakin, “Analysis of the Bloch equations for the nuclear magnetization model”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 123–140; Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 64–81

Citation in format AMSBIB
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\pages 123--140
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\jour Proc. Steklov Inst. Math. (Suppl.)
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